Heat is three things (let's keep it simple):
conduction
convection
radiation
conduction is when an atom at some point starts getting warmer, which means it starts jumping up and down on its spot more. This then convinces atoms near it to start doing the same, and on an on. If you have a metal bar (metal is a good heat conductor), and put one end in a fire, then slowly the entire bar will get hot, due in large part to conduction.
convection is where atoms get warmer but due to the substance they're in (a liquid or gas), they can move upwards, as they kick out more at the other atoms so become less dense (and thus rise). you can see this if you turn your radiator on and put your hand over the top of it -- you'll feel the warm air.
radiation is due to the excited particles shaking off photons of energy (photons are the particles of the electromagnetic spectrum, such as light, radiowaves, microwaves, x-rays and gamma rays). these are typically in the infra-red part of the spectrum for heat.
now, both conduction and convection require atoms or something in order for the phenomena to happen. space is (in a simplified sense) a vacuum, and so conduction and convection won't work. radiation, however (electromagnetic waves), doesn't require any medium, so can happily move across a vacuum, hence why we get light. we also get radiation from the sun too.
all electromagnetic waves travel at the same speed in vacuum, so radiation gets here just as fast as light.
finally, we only get a small amount of the radiation. it's given off all over the sun, like a concentric sphere moving outwards from the sun. we only make up a small part of that, so what part of the radiation passes through us is grabbed by us. the rest just travels on.